Distortion Property and Radius of Convexity for α-Starlike Functions

Abstract

본 논문은 Tepper가 발표한 Starlike 함수족에 관한 여러 가지 기하학적 성질들을 Miller, Mocanu, Reade가 소개한 α-Starlike 함수족들 S^(*)_(α), p-S^(*)_(α)(β) 과 p-S^(*)_(α)(β)으로 확장하는 것이 목적이다. 우리는 함수 f(z)=z+□b_(n)z^(n) 의 두 번째 계수 b_(2)를 0≤ b_(2)≤1으로 제한하여 위의 4종류의 함수족들에 대한 볼록성 반경 문제, d_(0)/ d^(*)의 하계 추정값, 왜곡 정리등의 기하학적 성질들을 찾아내고 증명한다.;With an aim of developing a new periodontal therapeutic modality, guided tissue regeneration (GTR), the drug loaded, biodegradable, biocompatible and porous poly (L-lactide) (PLLA) membranes were fabricated by an air-drying phase inversion technique, such as PLLA was dissolved in methylene chloride-ethyl acetate mixtures and cast on the knitted poly(glycolide) (PGA) meshes. Diffusion test and cell attachment test ascertained that membranes might be properly allow nutrition flux and be biocompatible. Drug release tests were performed with tetracycline loaded, flurbiprofen loaded or insulin loaded membranes. The drug release kinetics mainly depended upon hydrophobic- hydrophilic properties of the drugs and the release rate could be controlled by drug contents and drug loading method. Especially, tetracycline release from PLLA membranes could be Controlled by emulsifying tetracycline into PLLA matrix, by using salt form, by using polyvinyl alcohol lamination method and adding macromolecular drug. In in vitro biodegradation tests, PLLA membranes maintained 60% of their weight for 8 weeks, which were suggested as mechanical barriers for regeneration of periodontal tissue. In guided bone regeneration experiments, drug-loaded membranes significantly increased initial bone regenerative capacity in rat calvarial defects. These results suggest that the drug loaded porous PLLA membranes might be potential tools in improving current GTR efficacy.